public void testAddition() {

    PolynomialFunction p1 = new PolynomialFunction(new double[] {-2.0, 1.0});
    PolynomialFunction p2 = new PolynomialFunction(new double[] {2.0, -1.0, 0.0});
    checkNullPolynomial(p1.add(p2));

    p2 = p1.add(p1);
    checkPolynomial(p2, "-4.0 + 2.0 x");

    p1 = new PolynomialFunction(new double[] {1.0, -4.0, 2.0});
    p2 = new PolynomialFunction(new double[] {-1.0, 3.0, -2.0});
    p1 = p1.add(p2);
    assertEquals(1, p1.degree());
    checkPolynomial(p1, "-x");
  }
  public void testSubtraction() {

    PolynomialFunction p1 = new PolynomialFunction(new double[] {-2.0, 1.0});
    checkNullPolynomial(p1.subtract(p1));

    PolynomialFunction p2 = new PolynomialFunction(new double[] {-2.0, 6.0});
    p2 = p2.subtract(p1);
    checkPolynomial(p2, "5.0 x");

    p1 = new PolynomialFunction(new double[] {1.0, -4.0, 2.0});
    p2 = new PolynomialFunction(new double[] {-1.0, 3.0, 2.0});
    p1 = p1.subtract(p2);
    assertEquals(1, p1.degree());
    checkPolynomial(p1, "2.0 - 7.0 x");
  }
  /**
   * tests the value of a constant polynomial.
   *
   * <p>value of this is 2.5 everywhere.
   */
  public void testConstants() throws MathException {
    double[] c = {2.5};
    PolynomialFunction f = new PolynomialFunction(c);

    // verify that we are equal to c[0] at several (nonsymmetric) places
    assertEquals(f.value(0.0), c[0], tolerance);
    assertEquals(f.value(-1.0), c[0], tolerance);
    assertEquals(f.value(-123.5), c[0], tolerance);
    assertEquals(f.value(3.0), c[0], tolerance);
    assertEquals(f.value(456.89), c[0], tolerance);

    assertEquals(f.degree(), 0);
    assertEquals(f.derivative().value(0), 0, tolerance);

    assertEquals(f.polynomialDerivative().derivative().value(0), 0, tolerance);
  }
  /** This will test the quintic function f(x) = x^2(x-5)(x+3)(x-1) = x^5 - 3x^4 -13x^3 + 15x^2 */
  public void testQuintic() {
    double[] c = {0.0, 0.0, 15.0, -13.0, -3.0, 1.0};
    PolynomialFunction f = new PolynomialFunction(c);

    // verify that we are equal to c[0] when x=0
    assertEquals(f.value(0.0), c[0], tolerance);

    // now check a few other places
    assertEquals(0.0, f.value(5.0), tolerance);
    assertEquals(0.0, f.value(1.0), tolerance);
    assertEquals(0.0, f.value(-3.0), tolerance);
    assertEquals(54.84375, f.value(-1.5), tolerance);
    assertEquals(-8.06637, f.value(1.3), tolerance);

    assertEquals(f.degree(), 5);
  }
  /**
   * tests the value of a linear polynomial.
   *
   * <p>This will test the function f(x) = 3*x - 1.5
   *
   * <p>This will have the values <tt>f(0.0) = -1.5, f(-1.0) = -4.5, f(-2.5) = -9.0, f(0.5) = 0.0,
   * f(1.5) = 3.0</tt> and <tt>f(3.0) = 7.5</tt>
   */
  public void testLinear() throws MathException {
    double[] c = {-1.5, 3.0};
    PolynomialFunction f = new PolynomialFunction(c);

    // verify that we are equal to c[0] when x=0
    assertEquals(f.value(0.0), c[0], tolerance);

    // now check a few other places
    assertEquals(-4.5, f.value(-1.0), tolerance);
    assertEquals(-9.0, f.value(-2.5), tolerance);
    assertEquals(0.0, f.value(0.5), tolerance);
    assertEquals(3.0, f.value(1.5), tolerance);
    assertEquals(7.5, f.value(3.0), tolerance);

    assertEquals(f.degree(), 1);

    assertEquals(f.polynomialDerivative().derivative().value(0), 0, tolerance);
  }